We investigate the startling but real possibility that a reduction in calories can lead to a increase in longevity. In perhaps the simplest model, it may be evolutionarily optimal for a permanent reduction in the food supply to cause such an increase in longevity. However, it is impossible to account for all the data if fertility is a function of the food input alone. We propose, therefore, a more flexible model, incorporating both metabolic by-products and infectious disease. Where there is little infectious disease, the only effect of decreased food is to decrease the production of metabolic by-products, so individuals have increased life expectancy. On the other hand, where infectious disease is prevalent, decreased food intake increases mortality because the resulting reduction in immune function increases the impact of the disease. These predictions are consistent with an empirical model based on income per capita and calorie intake per capita across modern nations.